In this work, a novel constitutive model is developed within the framework of fractional plasticity to delineate the coupling between inelastic deformation and damage of quasi-brittle materials. Faced with the common challenge of determining plastic flow direction, we resort herein to the Riemann–Liouville definition of fractional derivatives, instead of introducing an additional plastic potential. The pre-peak hardening behavior is described using an exponential function, while the post-peak softening response is viewed as the consequence of material damage. For describing damage evolution, a damage criterion is constructed in terms of plastic volume dilation related to micro-crack growth. This is conducive to supply a new insight for describing the complex influence of the non-orthogonality of plastic flow on damage evolution. For numerical applications, a semi-implicit return mapping algorithm is proposed. The predictive performance of the model is evaluated by comparing numerical simulations with experimental data under various loading paths.

在这项工作中，在分数塑性框架内开发了一种新的本构模型，以描述非弹性变形与准脆性材料损伤之间的耦合。面对确定塑性流动方向的共同挑战，我们在此求助于分数导数的 Riemann-Liouville 定义，而不是引入额外的塑性势。峰值前硬化行为使用指数函数描述，而峰值后软化响应被视为材料损坏的结果。为了描述损伤演化，根据与微裂纹扩展相关的塑性体积膨胀来构建损伤准则。这有助于为描述塑性流动的非正交性对损伤演化的复杂影响提供新的见解。对于数值应用，提出了一种半隐式收益映射算法。模型的预测性能是通过将数值模拟与不同加载路径下的实验数据进行比较来评估的。